Broadcast control of multi-robot systems with norm-limited update vector

Abstract

This article addresses a problem in standard broadcast control framework which leads to an unstable solution in a certain motion-coordination task. First, the unstable phenomenon in a certain motion-coordination task is illustrated using standard broadcast control framework. This issue calls for modification to the standard broadcast control framework by limiting the norm of the update vector of robots’ positions into a constant value. Then, we demonstrate that the modified broadcast controller achieves the convergence with the probability of 1. Finally, we illustrate in numerical simulations that the modified broadcast controller can effectively solve the instability issue and also may improve the convergence time as compared to the standard broadcast controller.